An Optimal g-Guidance Scheme for Satellite Launch Vehicles

A closed-loop steering logic based on an optimal (2-guidance is developed here. The guidance system drives the satellite launch vehicle along a two- or three- dimensional trajectory for placing the payload into a specified circular orbit. The modified g-guidance algorithm makes use of the optimal required velocity vector, which minimizes the total impulse needed for an equivalent two-impluse transfer from the present state to the final orbit. The required velocity vector is defined as velocity of the vehicle on the hypothetical transfer orbit immediately after the application of the first impulse. For this optimal transfer orbit, a simple and elegant expression for the Q-matrix is derived. A working principle for the guidance algorithm in terms of the major and minor cycles, and also for the generation of the steering command, is outlined.

Determination of optimal trajectory under design constraints for a satellite launch vehicle

An optimal pitch steering programme of a solid-fuel satellite launch vehicle to maximize either (1) the injection velocity at a given altitude, or (2) the size of circular orbit, for a given payload is presented. The two-dimensional model includes the rotation of atmosphere with the Earth, the vehicle's lift and drag, variation of thrust with time and altitude, inverse-square gravitational field, and the specified initial vertical take-off. The inequality constraints on the aerodynamic load, control force, and turning rates are also imposed. Using the properties of the central force motion the terminal constraint conditions at coast apogee are transferred to the penultimate stage burnout. Such a transformation converts a time-free problem into a time-fixed one, reduces the number of terminal constraints, improves accuracy, besides demanding less computer memory and time. The adjoint equations are developed in a compact matrix form. The problem is solved on an IBM 360/44 computer using a steepest ascent algorithm. An illustrative analysis of a typical launch vehicle establishes the speed of convergence, and accuracy and applicability of the algorithm.

Launch Envelope Optimization of Virtual Sliding Target Guidance Scheme

This paper presents an optimization of the performance of a recently proposed virtual sliding target (VST) guidance scheme in terms of maximization of its launch envelope for three- dimensional (3-D) engagements. The objective is to obtain the launch envelope of the missile using the VST guidance scheme for different lateral launch angles with respect to the line of sight (LOS) and demonstrate its superiority over kinematics-based guidance laws like proportional navigation (PN). The VST scheme uses PN as its basic guidance scheme and exploits the relation between the atmospheric properties, missile aerodynamic characteristics, and the optimal trajectory of the missile. The missile trajectory is shaped by controlling the instantaneous position and the speed of a virtual target which the missile pursues during the midcourse phase. In the proposed method it is shown that an appropriate value of initial position for the virtual target in 3-D, combined with optimized virtual target parameters, can significantly improve the launch envelope performance. The paper presents the formulation of the optimization problem, obtains the approximate models used to make the optimization problem more tractable, and finally presents the optimized performance of the missile in terms of launch envelope and shows significant improvement over kinematic-based guidance laws. The paper also proposes modification to the basic VST scheme. Some simulations using the full-fledged six degrees-of-freedom (6-DOF) models are also presented to validate the models and technique used.

A Nonlinear Approach for Re-entry Guidance of Reusable Launch Vehicles Using Model Predictive Static Programming

A nonlinear suboptimal guidance scheme is developed for the reentry phase of the reusable launch vehicles. A recently developed methodology, named as model predictive static programming (MPSP), is implemented which combines the philosophies of nonlinear model predictive control theory and approximate dynamic programming. This technique provides a finite time nonlinear suboptimal guidance law which leads to a rapid solution of the guidance history update. It does not have to suffer from computational difficulties and can be implemented online. The system dynamics is propagated through the flight corridor to the end of the reentry phase considering energy as independent variable and angle of attack as the active control variable. All the terminal constraints are satisfied. Among the path constraints, the normal load is found to be very constrictive. Hence, an extra effort has been made to keep the normal load within a specified limit and monitoring its sensitivity to the perturbation.

Investigations on voltages and currents in the lightning protection system of the Indian satellite launch pad-I during a stroke interception

A reliable protection against direct lightning hit is very essential for satellite launch pads. In view of this, suitable protection systems are generally employed. The evaluation of efficacy of the lightning protection schemes among others requires an accurate knowledge of the consequential potential rise at the struck point and the current injected into soil at the earth termination. The present work has made a detailed effort to deduce these quantities for the lightning protection scheme of the Indian satellite launch pad-I. A reduced scale model of the system with a frequency domain approach is employed for the experimental study. For further validation of the experimental approach, numerical simulations using numerical electromagnetic code-2 are also carried out on schemes involving single tower. The study results on the protection system show that the present design is quite safe with regard to top potential rise. It is shown that by connecting ground wires to the tower, its base current and, hence, the soil potential rise can be reduced. An evaluation of an alternate design philosophy involving insulated mast scheme is also made. The potential rise in that design is quantified and the possibility of a flashover to supporting tower is briefly looked into. The supporting tower is shown to have significant induced currents.

Optimal Nonlinear Control and Estimation for a Reusable Launch Vehicle During Reentry Phase

In this paper a nonlinear optimal controller has been designed for aerodynamic control during the reentry phase of the Reusable Launch Vehicle (RLV). The controller has been designed based on a recently developed technique Optimal Dynamic Inversion (ODI). For full state feedback the controller has required full information about the system states. In this work an Extended Kalman filter (EKF) is developed to estimate the states. The vehicle (RLV) has been has been consider as a nonlinear Six-Degree-Of-Freedom (6-DOF) model. The simulation results shows that EKF gives a very good estimation of the states and it is working well with ODI. The resultant trajectories are very similar to those obtained by perfect state feedback using ODI only.

Suboptimal reentry guidance of a reusable launch vehicle using pitch plane maneuver

Using the recently developed model predictive static programming (MPSP) technique, a nonlinear suboptimal reentry guidance scheme is presented in this paper for a reusable launch vehicle (RLV). Unlike traditional RLV guidance, the problem considered over here is restricted only to pitch plane maneuver of the vehicle, which allows simpler mission planning and vehicle load management. The computationally efficient MPSP technique brings in the philosophy of trajectory optimization into the framework of guidance design, which in turn results in very effective guidance schemes in general. In the problem addressed in this paper, it successfully guides the RLV through the critical reentry phase both by constraining it to the allowable narrow flight corridor as well as by meeting the terminal constraints at the end of the reentry segment. The guidance design is validated by considering possible aerodynamic uncertainties as well as dispersions in the initial conditions. (C) 2010 Elsevier Masson SAS. All rights reserved.

Optimal explicit terminal guidance for a launch vehicle

It is observed that general explicit guidance schemes exhibit numerical instability close to the injection point. This difficulty is normally attributed to the demand for exact injection which, in turn, calls for finite corrections to be enforced in a relatively short time. The deviations in vehicle state which need corrective maneuvers are caused by the off-nominal operating conditions. Hence, the onset of terminal instability depends on the type of off-nominal conditions encountered. The proposed separate terminal guidance scheme overcomes the above difficulty by minimizing a quadratic penalty on injection errors rather than demanding an exact injection. There is also a special requirement in the terminal phase for the faster guidance computations. The faster guidance computations facilitate a more frequent guidance update enabling an accurate terminal thrust cutoff. The objective of faster computations is realized in the terminal guidance scheme by employing realistic assumptions that are accurate enough for a short terminal trajectory. It is observed from simulations that one of the guidance parameters (P) related to the thrust steering angular rates can indicate the onset of terminal instability due to different off-nominal operating conditions. Therefore, the terminal guidance scheme can be dynamically invoked based on monitoring of deviations in the lone parameter P.

Ascent Phase Trajectory Optimization of a Generic Launch Vehicle

Trajectory optimization of a generic launch vehicle is considered in this paper. The trajectory from launch point to terminal injection point is divided in to two segments. The first segment deals with launcher clearance and vertical raise of the vehicle. During this phase, a nonlinear feedback guidance loop is incorporated to assure vertical raise in presence of thrust misalignment, centre of gravity offset, wind disturbance etc. and possibly to clear obstacles as well. The second segment deals with the trajectory optimization, where the objective is to ensure desired terminal conditions as well as minimum control effort and minimum structural loading in the high dynamic pressure region. The usefulness of this dynamic optimization problem formulation is demonstrated by solving it using the classical Gradient method. Numerical results for both the segments are presented, which clearly brings out the potential advantages of the proposed approach.

Robust Reentry Guidance of a Reusable Launch Vehicle Using Model Predictive Static Programming

A robust suboptimal reentry guidance scheme is presented for a reusable launch vehicle using the recently developed, computationally efficient model predictive static programming. The formulation uses the nonlinear vehicle dynamics with a spherical and rotating Earth, hard constraints for desired terminal conditions, and an innovative cost function having several components with associated weighting factors that can account for path and control constraints in a soft constraint manner, thereby leading to smooth solutions of the guidance parameters. The proposed guidance essentially shapes the trajectory of the vehicle by computing the necessary angle of attack and bank angle that the vehicle should execute. The path constraints are the structural load constraint, thermal load constraint, bounds on the angle of attack, and bounds on the bank angle. In addition, the terminal constraints include the three-dimensional position and velocity vector components at the end of the reentry. Whereas the angle-of-attack command is generated directly, the bank angle command is generated by first generating the required heading angle history and then using it in a dynamic inversion loop considering the heading angle dynamics. Such a two-loop synthesis of bank angle leads to better management of the vehicle trajectory and avoids mathematical complexity as well. Moreover, all bank angle maneuvers have been confined to the middle of the trajectory and the vehicle ends the reentry segment with near-zero bank angle, which is quite desirable. It has also been demonstrated that the proposed guidance has sufficient robustness for state perturbations as well as parametric uncertainties in the model.

X-ray Structure of Gelonin at 1.8 Å Resolution

Gelonin is a single chain ribosome inactivating protein (RIP) with potential application in the treatment of cancer and AIDS. Diffraction quality crystals grown using PEG3350, belong to the space group P2(1), with it a = 49.4 Angstrom b = 44.9 Angstrom, c = 137.4 Angstrom and beta = 98.4 degrees, and contain two molecules in the asymmetric unit. Diffraction data collected to 1.8 Angstrom resolution has a R(m) value of 7.3%. Structure of gelonin has been solved by the molecular replacement method, using ricin A chain as the search model. Crystallographic refinement using X-PLOR resulted in a model for which the r.m.s deviations from ideal bond lengths and bond angles are 0.012 Angstrom and 2.7 degrees, respectively The final R-factor is 18.4% for 39,806 reflections for which I > 1.0 sigma(I).The C-alpha atoms of the two molecules in the asymmetric unit superpose to within 0.38 Angstrom for 247 atom pairs. The overall fold of gelonin is similar to that of other RIPs such as ricin A chain and alpha-momorcharin, the r.m.s.d. for C-alpha superpositions being 1.3 and 1.4 Angstrom, respectively The-catalytic residues (Glu166, Arg169 and Tyr113) in the active site form a hydrogen bond scheme similar to that observed in other RIPs. The conformation of Tyr74 in the active site, however, is significantly different from that in alpha-momorcharin. Three well defined water molecules are located in the active site cavity and one of them, X319, superposes to within 0.2 Angstrom of a corresponding water molecule in the structure of alpha-momorcharin. Any of the three could be the substrate water molecule in the hydrolysis reaction catalysed by gelonin.Difference electron density for a N-linked sugar moiety has been observed near only one of the two potential glycosylation sites in the sequence. The amino acid at position 239 has been established as Lys by calculation of omit electron density maps.The two cysteine residues in the sequence, Cys44 and Cys50, form a disulphide bond, and are therefore not available for disulphide conjugation with antibodies. Based on the structure, the region of the molecule that is involved in intradimer interactions is suggested to be suitable for introducing a Cys residue for purposes of conjugation with an antibody to produce useful immunotoxins.

Ethyl 1-(2-cyanoethyl)-3,5-dimethyl-1H-indole-2-carboxylate

The title compound, C16H18N2O2, is an important precursor in the synthesis of 1,2,3,4-tetrahydropyrazinoindoles, which show excellent antihistamine, antihypertensive and central nervous system depressant properties. The carbethoxy group attached to C2 and the planar cyanoethyl group attached to N1 make dihedral angles of 11.0(4) and 75.0(3)degrees, respectively, with the mean plane of the indole ring, The C-C=N chain is linear with a bond angle of 179.3 (4)degrees.

3-Phenylisoquinolin-1(2H)-one

The title compound, C15H11NO, consists of a planar isoquinolinone group to which a phenyl ring is attached in a twisted fashion [dihedral angle = 39.44 (4)degrees]. The crystal packing is dominated by intermolecular N-H center dot center dot center dot O and C-H center dot center dot center dot O hydrogen bonds which define centrosymmetric dimeric entitities.

Methyl 1H-1,2,3-triazole-4-carboxylate

The title compound, C4H5N3O2, features an essentially planar molecule (r.m.s. deviation for all non-H atoms = 0.013 angstrom). The crystal structure is stabilized by intermolecular N-H center dot center dot center dot O hydrogen bonds and pi-pi stacking interactions (centroid centroid distance 3.882 angstrom).